Efficient Two Photon Generation from an Atom in a Cavity

Abstract: Two-photon states are essential for quantum technologies such as metrology, lithography, and communication. One of the main methods of two-photon generation is based on parametric down-conversion, but this suffers from low efficiency and a large footprint. This work is a detailed investigation of an alternative approach: two-photon generation from an atom in a doubly resonant cavity. The system, consisting of an atom interacting with two modes of the cavity, is modelled by the Lindblad Master Equation. An approximate analytical solution is derived, using a novel approximation method, to determine the practically achievable limits on efficiency and brightness. The model also predicts the optimal cavity parameters for achieving these limits. For experimentally feasible parameters, the maximum efficiency turns out to be approximately $0.1\%$, which is about three orders of magnitude greater than that of parametric down-conversion-based methods. The optimal rate and efficiency for two-photon generation are achieved when the outcoupling rate of the cavity mode at the two-photon emission frequency matches the single-photon atom-field coupling strength. Moreover, the outcoupling rate of the cavity mode at the one-photon emission frequency for single photons should be minimized. The cavity field properties are also examined by studying the second-order correlation function at zero time delay and the Fano Factor. The quantum-jump framework, combined with Monte Carlo simulations, is used to characterize the mechanism of two-photon emission and the emission spectra of the cavity. Two-photon emission is demonstrated to be a rapid cascade process of quantum jumps, and the spectrum exhibits distinct peaks that correspond to transitions between the manifolds of the system.